Determining Coplanarity of four points

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Homework Help Overview

The discussion revolves around determining the coplanarity of four points in three-dimensional space, specifically the points A(3,1,0), B(2,-3,1), C(-1,0,4), and D(5,-6,-2).

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster questions whether to create vectors from the origin and expresses uncertainty about this approach. Other participants discuss the condition for coplanarity using vector operations and seek alternative methods due to their current understanding of vector multiplication.

Discussion Status

Participants are exploring various methods to determine coplanarity, including vector conditions and equations of planes. Some guidance has been provided regarding the use of plane equations, but there is no consensus on the best approach yet.

Contextual Notes

Some participants note that they have not yet learned vector multiplication, which affects their ability to apply certain methods. There is also discussion about how to define vectors, whether from the origin or between points.

jrotmensen
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How do you determine Coplanarity of four points?
I am given A(3,1,0), B(2,-3,1), C(-1,0,4), D(5,-6,-2).

Do i make vectors for each point from the origin? (But that wouldn't work would it? :()
Can anybody point me in the right direction?

Thanks!
 
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if a,b,c are coplanar vectors then
a.(bxc)=0
 
rock.freak667 said:
if a,b,c are coplanar vectors then
a.(bxc)=0

at this point, we haven't learned vector*vector multiplication.
is there any other way?

also, how should i get the vectors? displacement of the point from the origin? or displacement from one point to another??
 
Last edited:
The equation of any plane (that does not include the origin) can be written in the form Ax+ By+ Cz= 1. Replace x, y, and z by the coordinates of three of your points to get three equations to solve for A, B, and C. (If you can't, it is because the plane includes the origin- so try again with Ax+ By+ Cz= 0.)

Once you have the equation of the plane that contains three of the points, put the coordinates of the fourth point into that equation and see if they also satify the equation.
 

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